Questions: Lashonda wants to save money to open a tutoring center. She buys an annuity with a yearly payment of 489 that pays 3% interest, compounded annually. Payments will be made at the end of each year. Find the total value of the annuity in 7 years. Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formulas. [I]

Solution Steps

To find the total value of the annuity in 7 years, we can use the future value of an ordinary annuity formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] where:

• \( P \) is the yearly payment (\$489),
• \( r \) is the annual interest rate (3% or 0.03),
• \( n \) is the number of years (7).

We are given:

• Yearly payment \( P = 489 \)
• Annual interest rate \( r = 0.03 \)
• Number of years \( n = 7 \)

The future value \( FV \) of an ordinary annuity can be calculated using the formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \]

Substitute \( P = 489 \), \( r = 0.03 \), and \( n = 7 \) into the formula: \[ FV = 489 \times \frac{(1 + 0.03)^7 - 1}{0.03} \]

First, calculate \( (1 + 0.03)^7 \): \[ (1 + 0.03)^7 = 1.03^7 \approx 1.225043 \]

Next, calculate \( 1.225043 - 1 \): \[ 1.225043 - 1 = 0.225043 \]

Then, divide by the interest rate \( 0.03 \): \[ \frac{0.225043}{0.03} \approx 7.501433 \]

Finally, multiply by the yearly payment \( 489 \): \[ 489 \times 7.501433 \approx 3669.199 \]

Round the final value to the nearest cent: \[ 3669.199 \approx 3669.20 \]

Final Answer